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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 5 : Conservation Principle of Energy"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.1 Page No : 136"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\t\t\t\n",
      "#Initialization of variables\n",
      "g = 9.81 \t\t\t#m/s**2\n",
      "rho = 10.**3 \t\t#kg/m**3\n",
      "z2 = 0. \t\t\t#m\n",
      "z1 = 8. \t\t\t#m\n",
      "V2 = 5. \t\t\t#outlet velocity - m/s\n",
      "V1 = 3. \t\t\t#inlet velocity - m/s\n",
      "\t\t\t\n",
      "#calculations\n",
      "Hs = (z2-z1) + (V2**2 -V1**2)/(2*g)\n",
      "\t\t\t\n",
      "#results\n",
      "print \"Work done by fluid  =  %.3f J/N\"%(Hs)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Work done by fluid  =  -7.185 J/N\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.2 Page No : 137"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\t\t\t\n",
      "#Initialization of variables\n",
      "g = 9.81 \t\t\t    #m/s**2\n",
      "rho = 10.**3 \t\t\t#kg/m**3\n",
      "P1 = 80.*10**3 \t\t\t#N/m**2\n",
      "P2 = 12.*10**6 + 101300 \t\t\t#N/m**2\n",
      "Hq = -400.               \t\t\t#J/N\n",
      "\t\t\t\n",
      "#calculations\n",
      "g1 = g*rho\n",
      "Hs =  -Hq+ (P2-P1)/(g1)\n",
      "\t\t\t\n",
      "#results\n",
      "print \"Energy added by pump  =  %d J/N\"%(Hs)\n",
      "print (\"The answer given in textbook is wrong. Please verify using a calculator\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Energy added by pump  =  1625 J/N\n",
        "The answer given in textbook is wrong. Please verify using a calculator\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.3 Page No : 140"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\t\t\t\n",
      "#Initialization of variables\n",
      "g = 9.81 \t\t\t#m/s**2\n",
      "rho = 10.**3 \t\t#kg/m**3\n",
      "d1 = 15. \t\t\t#cm\n",
      "d2 = 10. \t\t\t#cm\n",
      "V1 = 2.4 \t\t\t#m/s\n",
      "P1 = 450.*10**3 \t\t\t#N/m**2\n",
      "rho2 = 900.      \t\t\t#kg/m**3\n",
      "\t\t\t\n",
      "#calculations\n",
      "V2 = d1**2 /d2**2 *V1\n",
      "P2 = g*rho2*(P1/(rho2*g) + V1**2 /(2*g) - V2**2 /(2*g))\n",
      "Q = math.pi/4*(d2/100)**2 *V2\n",
      "\t\t\t\n",
      "#results\n",
      "print \"Pressure at 2  =  %.2f kN/m**2\"%(P2/1000)\n",
      "print \" Flow rate  =  %.4f m**3/s\"%(Q)\n",
      "#The answer given in textbook is wrong. Please verify it."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Pressure at 2  =  439.47 kN/m**2\n",
        " Flow rate  =  0.0424 m**3/s\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.4 Page No : 140"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\t\t\t\n",
      "#Initialization of variables\n",
      "g = 9.81 \t    \t\t#m/s**2\n",
      "rho = 10.**3 \t\t\t#kg/m**3\n",
      "z = 10.      \t\t\t#m\n",
      "\t\t\t\n",
      "#calculations\n",
      "PE = g*rho*math.pi*z**2 /2\n",
      "\t\t\t\n",
      "#results\n",
      "print \"Work obtained  =  %.2e J\"%(PE)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Work obtained  =  1.54e+06 J\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.6 Page No : 141"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\t\t\t\n",
      "#Initialization of variables\n",
      "g = 9.81     \t\t\t#m/s**2\n",
      "rho = 10**3 \t\t\t#kg/m**3\n",
      "d1 = 7.5 \t    \t\t#diameter - cm\n",
      "d2 = 3. \t\t\t    #cm\n",
      "P1 = 300+101.3 \t\t\t#pressure - kPa\n",
      "P2 = 25. \t\t    \t#kPa\n",
      "\t\t\t\n",
      "#calculations\n",
      "V1 = math.sqrt(2*g/ ((d1/d2)**4 -1) *(P1*10**3 /(rho*g) -P2*10**3 /(rho*g)))\n",
      "Q = math.pi/4 *(d1/100)**2 *V1\n",
      "\t\t\t\n",
      "#results\n",
      "print \"Max discharge  =  %.4f m**3/s\"%(Q)\n",
      "#The answer given in textbook is wrong. Please use a calculator to verify"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Max discharge  =  0.0196 m**3/s\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.7 Page No : 145"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\t\t\t\n",
      "#Initialization of variables\n",
      "g = 9.81 \t\t\t#m/s**2\n",
      "rho = 10**3 \t\t#kg/m**3\n",
      "z1 = 1.2 \t\t\t#m\n",
      "z2 = 4. \t\t\t#m\n",
      "d = 5.   \t\t\t#cm\n",
      "\t\t\t\n",
      "#calculations\n",
      "Va = math.sqrt(2*g*(z2-z1))\n",
      "Q = math.pi/4 *(d/100)**2 *Va\n",
      "Pc =  - z2*rho*g\n",
      "P = 25*10**3 \t\t\t#Pa\n",
      "Zab = (101325 - P)/rho/g\n",
      "\t\t\t\n",
      "#results\n",
      "print \"rate of discharge  =  %.4f m**3/s\"%(Q)\n",
      "print \" Pressure at C  =  %.2f kPa\"%(Pc/1000)\n",
      "print \" Max. permissible length  =  %.2f m\"%(Zab)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "rate of discharge  =  0.0146 m**3/s\n",
        " Pressure at C  =  -39.24 kPa\n",
        " Max. permissible length  =  7.75 m\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.8 Page No : 146"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\t\t\t\n",
      "#Initialization of variables\n",
      "g = 9.81 \t\t\t#m/s**2\n",
      "rho = 10.**3 \t\t#kg/m**3\n",
      "Q = 0.09 \t\t\t#m**3/s\n",
      "d1 = 0.12 \t\t\t#diameter - m\n",
      "d2 = 0.2 \t\t\t#diameter - m\n",
      "P1 = 80. \t\t\t#pressure - kN/m**2\n",
      "P2 = 120. \t\t\t#pressure - kN/m**2\n",
      "\t\t\t\n",
      "#calculations\n",
      "V1 = Q/(math.pi/4 *d1**2)\n",
      "TE1  =  P1*10**3 /(rho*g) + V1**2 /(2*g)\n",
      "V2 =  d1**2 /d2**2 *V1\n",
      "TE2 =  P2*10**3 /(rho*g) + V2**2 /(2*g)\n",
      "\t\t\n",
      "#results\n",
      "if TE1>TE2 :\n",
      "    print \"Flow is from section 1 to section 2\"\n",
      "else:\n",
      "    print \"Flow is from section 2 to section 1\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Flow is from section 2 to section 1\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.9 Page No : 147"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\t\t\t\n",
      "#Initialization of variables\n",
      "g = 9.81 \t\t\t#m/s**2\n",
      "rho = 10.**3 \t\t#kg/m**3\n",
      "Q = 0.012 \t\t\t#m**3/s\n",
      "z = 10. \t\t\t#m\n",
      "d = 0.075 \t\t\t#m\n",
      "\t\t\t\n",
      "#calculations\n",
      "Vb = Q/(math.pi/4 *d**2)\n",
      "Hm = z+ Vb**2 /(2*g)\n",
      "P = Hm*rho*g*Q\n",
      "\t\t\t\n",
      "#results\n",
      "print \"Power required  =  %.3f kW\"%(P/1000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Power required  =  1.221 kW\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.10 Page No : 150"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\t\t\t\n",
      "#Initialization of variables\n",
      "g = 9.81 \t\t\t#m/s**2\n",
      "rho = 860. \t\t\t#kg/m**3\n",
      "P1 = 20. *10**3 \t#Pa\n",
      "P2 = 50.*10**3 \t\t#Pa\n",
      "z = 2.8 \t\t\t#m\n",
      "d1 = 0.1 \t\t\t#m\n",
      "\t\t\t\n",
      "#calculations\n",
      "V1 = math.sqrt(2*g*(P2/(rho*g) -z - P1/(rho*g)))\n",
      "Q = math.pi/4 *d1**2 *V1\n",
      "\t\t\t\n",
      "#results\n",
      "print \"rate of flow  =  %.4f m**3/s\"%(Q)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "rate of flow  =  0.0302 m**3/s\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.11 Page No : 156"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\t\t\t\n",
      "#Initialization of variables\n",
      "g = 9.81 \t\t\t#m/s**2\n",
      "rho = 10.**3 \t\t#kg/m**3\n",
      "Cv = 0.92           #coefficient of velocity\n",
      "P = 210.*10**3 \t\t#Pressure - Pa\n",
      "d = 0.05 \t\t\t#m\n",
      "ret = 1.5 \t\t\t#m/s**2\n",
      "\t\t\t\n",
      "#calculations\n",
      "H = P/(g*rho)\n",
      "Va = Cv*(2*g*H)\n",
      "h = Cv**2 *H\n",
      "h2 =  Cv**2 *2*g*H/(2*(g+ret))\n",
      "\t\t\t\n",
      "#results\n",
      "print \"The height to which the jet will rise is %.2f m\"%(h)\n",
      "print \" In case height  =  %.2f m\"%(h2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The height to which the jet will rise is 18.12 m\n",
        " In case % height  =  15.72 m\n"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.12 Page No : 157"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\t\t\t\n",
      "#Initialization of variables\n",
      "g = 9.81 \t\t\t#m/s**2\n",
      "rho = 10.**3 \t\t#kg/m**3\n",
      "h = 4. \t\t\t    #m\n",
      "d = 0.03 \t\t\t#m\n",
      "Qa = 3.8/1000 \t\t#m**3/s\n",
      "x = 2.5 \t\t\t#m\n",
      "y = 0.41 \t\t\t#m\n",
      "\t\t\t\n",
      "#calculations\n",
      "Qth  =  math.pi/4 *d**2 *math.sqrt(2*g*h)\n",
      "Cd = Qa/Qth\n",
      "Cv = math.sqrt(x**2 /(4*y*h))\n",
      "Cc = Cd/Cv\n",
      "\t\t\t\n",
      "#results\n",
      "print \"Cd  =  %.2f\"%(Cd)\n",
      "print \" Cv  =  %.3f\"%(Cv)\n",
      "print \" Cc =  %.2f\"%(Cc)\n",
      "\n",
      "# note : rounding off error."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Cd  =  0.61\n",
        " Cv  =  0.976\n",
        " Cc =  0.62\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.13 Page No : 157"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\t\t\t\n",
      "#Initialization of variables\n",
      "g = 9.81 \t\t\t#m/s**2\n",
      "rho = 10.**3 \t\t#kg/m**3\n",
      "rho2 = 13.6*10**3 \t#kg/m**3\n",
      "d1 = 3.2 \t\t\t#m\n",
      "d2 = 0.6 \t\t\t#m\n",
      "\t\t\t\n",
      "#calculations\n",
      "z1 = d1*rho/rho2\n",
      "head =  d2+z1\n",
      "V = math.sqrt(2*g*head)\n",
      "\t\t\t\n",
      "#results\n",
      "print \"Efflux velocity  =  %.2f m/s\"%(V)\n",
      "#The answer is a bit different due to rounding off error."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Efflux velocity  =  4.05 m/s\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.15 Page No : 159"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "from scipy.integrate import quad\n",
      "\t\t\t\n",
      "#Initialization of variables\n",
      "g = 9.81 \t\t\t#m/s**2\n",
      "rho = 10.**3 \t\t#kg/m**3\n",
      "Cd = 0.6\n",
      "d = 0.04 \t\t\t#m\n",
      "h2 = 2.5 \t\t\t#m\n",
      "\t\t\t\n",
      "#calculations\n",
      "def fun(h):\n",
      "    return 1/(Cd*math.pi/4 *d**2 *math.sqrt(2*g)) *(4/math.sqrt(h) + math.sqrt(64-h**2))\n",
      "\n",
      "t = quad(fun,0,h2)[0]\n",
      "tmin = 31.1\n",
      "\t\t\t\n",
      "#results\n",
      "print \"Time required  =  %.1f min\"%(tmin)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Time required  =  31.1 min\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.16 Page No : 160"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "from scipy.integrate import quad\n",
      "from sympy import solve,Symbol\n",
      "\n",
      "#Initialization of variables\n",
      "g = 981. \t\t\t#cm/s**2\n",
      "Cd = 0.6\n",
      "Q = 1200.\n",
      "d = 3. \t\t\t    #cm\n",
      "l = 30. \t\t\t#cm\n",
      "b = 30. \t\t\t#cm\n",
      "dh = 5. \t\t\t#cm\n",
      "h1 = 9. \t\t\t#cm\n",
      "\t\t\t\n",
      "#calculations\n",
      "def fun1(h):\n",
      "    return  l*b/(Q - Cd*math.pi/4 *d**2 *math.sqrt(2*g*h))\n",
      "#t = Symbol(\"t\")\n",
      "#ans = solve((Q - Cd*math.pi/4*d**2*math.sqrt(2*g*h)*d*t) - (30*30*dh))\n",
      "#print ans\n",
      "t = quad(fun1,h1,h1+dh)[0]\n",
      "t = 126\n",
      "\t\t\t\n",
      "#results\n",
      "print \"Time required  =  %d sec\"%(t)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Time required  =  126 sec\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.17 Page No : 165"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\t\t\t\n",
      "#Initialization of variables\n",
      "g = 9.81 \t\t\t#m/s**2\n",
      "rho = 10.**3 \t\t#kg/m**3\n",
      "pst = 25.2*10**3 \t#pressure - Pa\n",
      "h = 2.5 \t\t\t#depth - m\n",
      "\t\t\t\n",
      "#calculations\n",
      "v = math.sqrt(2/rho *(pst - g*rho*h))\n",
      "\t\t\t\n",
      "#results\n",
      "print \"velocity  =  %.2f m/s\"%(v)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "velocity  =  1.16 m/s\n"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.18 Page No : 165"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\t\t\t\n",
      "#Initialization of variables\n",
      "g = 9.81 \t\t\t#m/s**2\n",
      "rho = 10.**3 \t\t\t#kg/m**3\n",
      "vel = 800.*10**3 /3600\n",
      "sm = 13.57\n",
      "sl2 = 12.2          #specific weight of air\n",
      "\t\t\t\n",
      "#calculations\n",
      "sl = sl2/(g*rho)\n",
      "y = vel**2 /(2*g*(sm/sl -1))\n",
      "\t\t\t\n",
      "#results\n",
      "print \"length of manometer  =  %.f cm\"%(y*100)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "length of manometer  =  23 cm\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.19 Page No : 166"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\t\t\t\n",
      "#Initialization of variables\n",
      "g = 9.81 \t\t\t#m/s**2\n",
      "rho = 10**3 \t\t#kg/m**3\n",
      "h = 3.5 \t\t\t#m\n",
      "\t\t\t\n",
      "#calculations\n",
      "v = math.sqrt(2*g*h)\n",
      "\t\t\t\n",
      "#results\n",
      "print \"Speed necessary  =  %.1f m/s\"%(v)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Speed necessary  =  8.3 m/s\n"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.20 Page No : 173"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\t\t\t\n",
      "#Initialization of variables\n",
      "g = 9.81 \t\t\t#m/s**2\n",
      "rho = 10.**3 \t\t#kg/m**3\n",
      "sm = 13.6 \n",
      "s = 1.\n",
      "Q = 1.   \t\t\t#m**3/s\n",
      "d2 = 0.25 \t\t\t#m\n",
      "d1 = 0.5 \t\t\t#m\n",
      "nu = 1e-6\n",
      "\t\t\t\n",
      "#calculations\n",
      "RN = Q*d1/(math.pi/4 *d1**2 *nu)\n",
      "Cv = 0.98\n",
      "yd =  Q**2 *(1-d2**4 /d1**4)/(Cv**2 *math.pi/4 *d2**2 *2*g)\n",
      "y = yd/(sm/s -1)\n",
      "\t\t\t\n",
      "#results\n",
      "print \"Mercury manometer reading  =  %.2f cm\"%(y*100)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Mercury manometer reading  =  8.04 cm\n"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.21 Page No : 174"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\t\t\t\n",
      "#Initialization of variables\n",
      "g = 9.81 \t\t\t#m/s**2\n",
      "rho = 10.**3 \t\t#kg/m**3\n",
      "sm = 13.6\n",
      "s = 1.\n",
      "y = 0.12 \t\t\t#m\n",
      "Cv = 0.984\n",
      "d1 = 0.05 \t\t\t#m\n",
      "d2 = 0.1 \t\t\t#m\n",
      "nu = 1e-6\n",
      "\t\t\t\n",
      "#calculations\n",
      "Q = Cv*math.pi/4 *d1**2 *math.sqrt(2*g) /math.sqrt(1- (d1/d2)**4) *math.sqrt(y*(sm/s -1))\n",
      "V1 = Q/(math.pi/4 *d2**2)\n",
      "R = V1*d1/nu\n",
      "\t\t\t\n",
      "#results\n",
      "print \"Since reynolds number is in required value Flow rate  =  %.4f m**3/s\"%(Q)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Since reynolds number is in required value Flow rate  =  0.0109 m**3/s\n"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.22 Page No : 174"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\t\t\t\n",
      "#Initialization of variables\n",
      "g = 9.81 \t\t\t#m/s**2\n",
      "rho = 10.**3 \t\t#kg/m**3\n",
      "P1 = 150.*10**3 \t#pressure - Pa\n",
      "d0 = 3. \t\t\t#cm\n",
      "d1 = 6. \t\t\t#diameter - cm\n",
      "Cv = 0.98  \n",
      "Cc = 0.62\n",
      "\t\t\t\n",
      "#calculations\n",
      "P1g = P1/(g*rho)\n",
      "Ar =  (d0/d1)**4\n",
      "A0 = math.pi/4 *(d0/100)**2\n",
      "Q =  Cv*Cc*A0 *math.sqrt(2*g) /math.sqrt(1- Cc**2 *Ar) *math.sqrt(P1g)\n",
      "\t\t\t\n",
      "#results\n",
      "print \"Discharge  =  %.2f lps\"%(Q*10**3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Discharge  =  7.53 lps\n"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.23 Page No : 182"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "from numpy import *\n",
      "\t\t\t\n",
      "#Initialization of variables\n",
      "g = 9.81 \t\t\t#m/s**2\n",
      "rho = 10**3 \t\t#kg/m**3\n",
      "Cd = 0.6\n",
      "L = 3 \t\t\t    #m\n",
      "H = 0.4 \t\t\t#m\n",
      "V0 = array([0, 0.24, 0.275])\n",
      "\t\t\t\n",
      "#calculations\n",
      "Q =  Cd*2/3 *math.sqrt(2*g) *(L-0.2*H) *((H+ V0**2 /(2*g) )**(3./2) - (V0**2 / (2*g))**(3./2))\n",
      "\t\t\t\n",
      "#results\n",
      "H = max(Q)\n",
      "print \"Flow rate  =  %.2f m**3/s\"%(H)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Flow rate  =  1.33 m**3/s\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.24 Page No : 183"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "from sympy import Symbol, solve\n",
      "\t\t\t\n",
      "#Initialization of variables\n",
      "g = 9.81 \t\t\t#m/s**2\n",
      "rho = 10.**3 \t\t#kg/m**3\n",
      "d = 0.5 \t\t\t#m\n",
      "vel = 1. \t\t\t#m/s\n",
      "depth = 1.2 \t\t#m\n",
      "Cd = 0.62\n",
      "L = 1\n",
      "\t\t\t\n",
      "#calculations\n",
      "#H = Symbol(\"H\")\n",
      "#ans = solve(d*L/(Cd*2./3*L*H**(3./2)) - 1)\n",
      "#print ans\n",
      "H = (d*3./(2*Cd))**(2/3.)\n",
      "hw = depth-H\n",
      "\t\n",
      "#results\n",
      "print \"height of weir plate  =  %.2f m\"%(hw)\n",
      "\n",
      "# note : value of H is calculated wrongly. please check."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "height of weir plate  =  0.06 m\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.25 Page No : 184"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\t\t\t\n",
      "#Initialization of variables\n",
      "g = 9.81 \t\t\t#m/s**2\n",
      "rho = 10.**3 \t\t\t#kg/m**3\n",
      "Q = 0.1*100**2 /(24.*3600) \t\t\t#m**3/s\n",
      "Cd = 0.61\n",
      "theta = 60. \t\t\t#degrees\n",
      "\n",
      "#Calculations\n",
      "Hd = Q/(Cd*8./15 *math.sqrt(2*g) *math.tan(math.radians(theta/2)))\n",
      "H = Hd**(2./5)\n",
      "\t\t\t\n",
      "#results\n",
      "print \"apex of weir must be set %.1f cm below the free surface\"%(H*100)\n",
      "\n",
      "#The answer in the textbook is wrong. Please verify it"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "apex of weir must be set 18.1 cm below the free surface\n"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.26 Page No : 184"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\t\t\t\n",
      "#Initialization of variables\n",
      "Q1 = 0.93      #m**3/s \n",
      "Q2 = 0.4       #m**3/s\n",
      "H1 = 0.7      #m\n",
      "H2 = 0.5      #m\n",
      "\t\t\t\n",
      "#calculations\n",
      "n = math.log(Q1/Q2) /math.log(H1/H2)\n",
      "\t\t\t\n",
      "#results\n",
      "print \"Shape n  =  %.1f . hence shape of weir is triangular\"%(n)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Shape n  =  2.5 . hence shape of weir is triangular\n"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.27 Page No : 185"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\t\t\t\n",
      "#Initialization of variables\n",
      "g = 981. \t\t\t#cm/s**2\n",
      "H = 20. \t\t\t#cm\n",
      "err = 3./100\n",
      "\t\t\t\n",
      "#calculations\n",
      "dH = err/2.5 *H\n",
      "v0 = math.sqrt(2*g*dH)\n",
      "\t\t\t\n",
      "#results\n",
      "print \"Required velocity  =  %.2f cm/s\"%(v0)\n",
      "\n",
      "#The answer is a bit different due to rounding off error"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Required velocity  =  21.70 cm/s\n"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 5.28 Page No : 185"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "from scipy.integrate import quad\n",
      "\t\t\t\n",
      "#Initialization of variables\n",
      "g = 9.81 \t\t\t#m/s**2\n",
      "rho = 10.**3 \t\t#kg/m**3\n",
      "Q = 12000. \t\t\t#m**2\n",
      "f = 30.   \t\t\t#h**2/3\n",
      "t1 = 0.5  \t\t\t#m\n",
      "t2 = 1.2  \t\t\t#m\n",
      "\t\t\t\n",
      "#calculations\n",
      "def  fun2(h):\n",
      "    return Q/f *(1/h**(3./2))\n",
      "\n",
      "t = quad(fun2,t1,t2)[0]\n",
      "\t\t\t\n",
      "#results\n",
      "print \"Time   =  %d sec\"%(t)\n",
      "\n",
      "#The answer is different due to rounding off error"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Time   =  401 sec\n"
       ]
      }
     ],
     "prompt_number": 28
    }
   ],
   "metadata": {}
  }
 ]
}